Half life question

1. The problem statement, all variables and given/known data
A radioactive source emits alpha particles at a constant rate 3.5x10^6 s^-1. The particles are collected for a period of 40 days.
BY reference to the half life of the source, suggest why it may be assumed that rate of emission of alpha particles remain constant?

3. The attempt at a solution
Since the decay constant is very small, ##A_o-A \approx A_o## where ##A_o## is initial activity and ##A## is a decrease in activity over a significant period of time.

Since Activity remains constant, the rate of emission remains constant.

I cannot, however, find a way to incorporate the half-life into the answer which the question specifically mentions. I am aware of the relation between decay constant and half-life, but for this situation, I cannot develop a clear logic which involves the half-life of the source. More specifically how does rate of emission remains constant if a half-life is high?

Good questions. To which I would add: What is the mass of the source and its atomic weight, or equivalently the number of gram-moles it contains? A flux of 3.5x10^6 particles per second is one thing if it's coming from a 5 kg source, and something else if it's produced by 1 mg.

Good questions. To which I would add: What is the mass of the source and its atomic weight, or equivalently the number of gram-moles it contains? A flux of 3.5x10^6 particles per second is one thing if it's coming from a 5 kg source, and something else if it's produced by 1 mg.

I think I'd approach it this way. Assume the source is reasonably pure and macroscopic--say a few grams. Pick a credible mass number, and estimate the number of alpha emitters in the source. Compare that number to the number of decays, at the specified rate, in one second, an hour, a day, 40 days . . . (Note that whatever the half life, the rate can only go down; so assuming a constant rate gives an upper bound on the actual number of decays in each period.)

A radioactive source emits alpha particles at a constant rate 3.5x10^6 s^-1. The particles are collected for a period of 40 days.
BY reference to the half life of the source, suggest why it may be assumed that rate of emission of alpha particles remain constant?

The wording of this question is atrocious. Are you sure you have quoted it exactly? Is it a translation?
The time for which the particles are collected provides no information in itself. I can only suppose it intends to convey that the collection rate appeared constant for 40 days.